In this post, we will see the book Theory Of Anisotropic Shells by V. A. Ambartsumyan.

About the book

Shells are widely used as structural elements in modem construction engineering, aircraft construction, shipbuilding, rocket construction, etc. A careful study of the shells used in engineering leads to the conclusion that they are most often anisotropic (naturally or structurally) and in many cases are anisotropic and laminar.

Despite the large number of articles appearing in journals, there is as yet not one book devoted to the theory of anisotropic laminar shells. In the present book the author partially fills this gap. The text is based on the author’s investigations over the last few years. It consists of the following divisions: (a) fundamental equations of the theory of elasticity of an anisotropic body in curvilinear coordinates; (b) general theory of anisotropic laminar shells; (c) membrane theory of anisotropic shells; (d) theory of symmetrically loaded anisotropic shells of revolution; (e) anisotropic cylindrical shells; (f) shallow anisotropic shells; (g) new theories of aniso­tropic shells and plates.

The book does not deal with the undeniably important problems of non­ linear theory, the theories of stability and vibration, as well as temperature problems of anisotropic laminar shells. Nor does it deal with problems associ­ated with plastic and elastic-plastic deformations of the material of the shell layers, since these problems have not been adequately investigated.
Within each chapter the formulas have a two-part enumeration. Where reference is made to the formulas of preceding chapters a three-part enumer­ation is used (the first digit referring to the chapter).

The book was translated from Russian by was published under NASA Technical Translation series.

Credits to original uploader.

You can get the book here.

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Contents

CHAPTER I
FUNDAMENTAL EQUATIONS OF THE THEORY OF ELASTICITY OF AN ANISOTROPIC BODY IN CURVILINEAR COORDINATES

Section 1. Some Remarks on Curvilinear Coordinates in Space 1
Section 2. Deformation Components and Differential Equations of Equilibrium in the Triorthogonal System of Curvilinear Coordinates 4
Section 3. Curvilinear Anisotropy. Generalized Hooke’s Law 7
Section 4. Transformation of Elastic Constants with Rotation of the Coordinate System 12
Section 5. Elastic Constants for Certain Anisotropic Materials 14

CHAPTER II
FUNDAMENTAL EQUATIONS OF THE THEORY OF SHELLS CONSISTING OF AN ARBITRARY NUMBER OF ANISOTROPIC LAYERS

Section 1. Basic Concepts, Initial Relationships and Hypotheses 18
Section 2. Displacements and Deformations 22
Section 3. Equations of Continuity of Deformations of the Coordinate
Surface 25
Section 4. Stressesin Layers 26
Section 5. Conditions of Contact of Adjacent Layers 28
Section 6. Internal Forces and Moments 29
Section 7. Equilibrium Equations 31
Section 8. Potential Energy of Deformation 33
Section 9. Elasticity Relationships 35
Section 10. Boundary Conditions 38
Section 11. Additional Remarks Concerning the Conditions of Contact
of Adjacent Layers and the Conditions at the Outer Surfaces of a Shell 40
Section 12. Special Cases of Anisotropy of the Material of the Shell Layers 43
Section 13. Shells Consisting of an Odd Number of Layers Symmetrically Arranged Relative in the Coordinate Surface 45
Section 14. Single-Layer Anisotropic Shells 50
Section 15. Further Remarks Concerning Elasticity Relationships 55
Section 16. Calculation of Stiffnesses for Arbitrary Directions 58

CHAPTER III
MEMBRANE THEORY OF ANISOTROPIC SHELLS

Section 1. General I’remises and Initial Relationships in the Membrane Theory of Single-Layer Isotropic Shells 61
Section 2. Boundary Conditions 64
Section 3. Area of Applicability of the Membrane Theory 65
Section 4. Fundamental Equations of the Membrane Theory of Symmetrically loaded Shells of Revolution 66
Section 5. Examples of Calculation of Symmetrically Loaded Shells
Of Revolution 73
Section 6. Evaluation of Results Obtained in the Preceding Section 86
Section 7. Continuation of Section 5 87
Section 8. An Arbitrarily Loaded Cylindrical Shell of Arbitrary Shape 95
Section 9. Some Remarks Concerning the Membrane Theory of Anisotropic Laminar Shells 104

CHAPTER IV
SYMMETRICALLY LOADED ANISOTROPIC SHELLS OF REVOLUTION

Section 1. Basic Premises. Initial Relationships and Equations 109
Section 2. Equations of Solution and Design Formulas 113
Section 3. Shells of Revolution Consisting of an Odd Number of Layers Symmetrically Arranged Relative to the Median Surface of the Shell 117
Section 4. Single-Layer Shells of Revolution 120
Section 5. Reduction of the System of Equations in (3.16) and
(3.17) to a Single Equation. A Particular Solution of the
Inhomogeneous Equation 121
Section 6. Asymptotic Integration of the Equation of Solution (5.9) 124
Section 7. Internal Forces, Moments, Stresses and Displacements 132
Section 8. Edge Effect in Anisotropic Shell 136
Section 9. Long Shells of Revolution 26 139
Section 10. Examples of Calculation of Long Shells of Revolution 143
Section 11. Solution of a Few Problems of Shells of Revolution of Zere Gaussian Curvature Consisting of an Arbitrary Number of Layers 166
Section 12. Anisotropic Cylindrical Shells of Revolution Reinforced
by Lateral Ribs 177

CHAPTER V
ANISOTROPIC CYLINDRICAL SHELLS

Section 1. Basic Premises. Initial Relationships and Equations 195
Section 2. System of Differential Equations of Solution in Displacements 198
Section 3. Cylindrical Shells Consisting of an Arbitrary Number of Orthotropic Layers 201
Section 4. Engineering Theory of Cylindrical Shells Consisting of an Arbitrary Number of Anisotropic Layers 208
Section 5. Continuation of Section 4. 214
Section 6. Cylindrical Shells Consisting of an Odd Number of Homogeneous Anisotropic Layers Symmetrically Arranged Relative to the Median Surface 224
Section 7. Engineering Theory of Cylindrical Shells Consisting of an Odd Number of Homogeneous Anisotropic Layers Symmetrically Arranged Relative to the Median Surface 228
Section 8. Continuation of Section 7. 232
Section 9. Integration of the Equations of Engineering Theory of a Cylindrical Sne!l by the Method of Double Trigonometric Series 240
Section 10. Integration of Equations in the Engineering Theory of Cylindrical Shells by the Method of Single Trigonometric 265

CHAPTER VI
SHALLOW ANISOTROPIC SHELLS

Section 1. Basic Premises. Initial Relationships and Equations 277
Section 2. Equations of Solution and Design Formulas 280
Section 3. Shells Consisting of an Odd Number of Homogeneous Anisotropic Layers Symmetrically Arranged Relative to the Median Surface 285
Section 4. Extremely Shallow Shells. Basic Premises, Initial Relationships and Equations 288
Section 5. Equations of Solution and Design Formulas in the Theory of Extremely Shallow Shells Consisting of an Arbitrary Number of Anisotropic Layers 292
Section 6. Equations of Solution and Design Formulas in the Theory of Extremely Shallow Shells Consisting of an Odd Number of Homogeneous Anisotropic Layers Symmetrically Arranged Relative to the Median Surface 300
Section 7. Integration of the Equations of Solution in the Theory of Extremely Shallow Orthotropic Shells 306

CHAPTER VII
NEW THEORIES OF ANISOTROPIC SHELLS AND PLATES

Section 1. Basic Premises and Hypotheses 315
Section 2. Theory of Orthotropic Plates 316
Section 3. Theory of Bending of a Plate Possessing Cylindrical Anisotropy 328
Section 4. Approximate Theory of an Anisotropic Plate Considering Transverse Shear 332
Section 5. Another Approximate Theory of Anisotropic Plates 336
Section 6. Examples of Plate Calculations 342
Section 7. Theory of Extremely Shallow Anisotropic Shells 358
Section 8. Approximate Theory of an Extremely Shallow Shell Considering Transverse Shear 365
Section 9. Another Approximate Theory for an Extremely Shallow Shell 368
Section 10. Example of Calculation of a Shell 372
Section 11. Theory of Extremely Shallow Laminar Orthotropic Shells. 376
Section 12. Examples of Calculation of Laminar Shells and Plates 386